Packing Fractions (Neutron spin structure functions from RSS data)

Packing Fractions and Dilution Factors

General Information

Latest proton DFs: Feb 02, 2006
Latest deuteron DFs: Dec 11, 2006
History of RSS Dilution Factors (updated in Dec 2006).

Status and results (Dec. 18, 2007)

Study of deuteron DF Systematics uncertainty due to the nucleon model (updated from oct 30, 2007)

Found that the results posted on oct30, 2007 were incorrect because the MC used to get those results was a TEST MC that was used to get the results for the DF systematics due to deuteron model. (In this version, values from Peter's deuteron models were increased by several %. see my jul03,2007 report for details.) Apparently, I forgot to change the source code back to the 'regular' version. Because of this, I needed to redo my DF systematic calculations originally posted on oct30,2007. Note that the procedures are the same, but the numbers are different.

<>We used similar procedures for the proton systematics (feb16, 2006) to get the deuteron systematics uncertainty due to nucleon model (A>2). The scalein value of 1.04 (0.96) for high P (low P) run was used, and the DFs were calculated. I assumed that the avg PFs for this case would be almost unchanged, as we saw for the proton case (see dec20, 2005), so I did not calculate the new PFs this time. The ratio of new DF to the original (scalein=1.0) is calculated. The avg ratio for high P (low W) for W>1100 is 1.022 +/- 0.002 while for low P (high W) it is 1.030 +/- 0.002. The weighted average of the two is 1.027 +/- 0.001, so the systematics uncertainty is 2.7%.

Like the proton results on feb16, 2006, the syst uncertaintainties for low P and high P given above are close to each other.

overall deuteron DF systematics (updated from Sep.25 result)

Using the above systematic uncertainty of 2.7% due to A>2 nucleon model, the total deuteron DF systematic uncertainty is calculated. It is given by

delta_df = sqrt[(A*(delta_deuteron/deuteron))^2 + (B*(delta_nuclear/nuclear))^2 + (C*(delta_pf/pf))^2),
where A, B, and C are the scaling factors.

Deuteron model: Found that the relative DF systematic uncertainty due to deuteron model is 2.6% or less (Jul 03, 2007). A=1.0
Nuclear model: 4.0% change in the nuclear model (A>2) (=delta_nuclear/nuclear) yields 2.7% change in DF. B=0.675.
PF: Found that delta_pf/pf= ~8.2% (Sep25,2007). According to my Jul25,2005 report, 2.4% relative change in PF leads to 1.0% relative change in DF for deuteron target. Therefore, C is estimated to be C=1.0/2.4=0.417. The result is given below:

delta_df= sqrt[(2.6%)^2 + (2.7%)^2 + (0.417*8.2%)^2]= 5.07%

In addition, we can add other systematics due to run selection (0.5%, Jul25,2005) and PF extraction methods (0.4% Aug16,2005). The total DF systematics then becomes 5.11%.

Status and results (Oct. 30, 2007) --- Incorrect results: See Dec18, 2007 above

Study of deuteron DF Systematics uncertainty due to the nucleon model (preliminary)

We used similar procedures for the proton systematics (feb16, 2006) to get the deuteron systematics uncertainty due to nucleon model (A>2). The scalein value of 1.04 (0.96) for high P (low P) runs was used, and the DFs were calculated. I assumed that the avg PFs for this case would be almost unchanged, as we saw for the proton case (see dec20, 2005), so I did not calculate the new PFs this time. The ratio of new DF to the original (scalein=1.0) is calculated. The avg ratio for high P (low W) is 1.0090 +/- 0.0021 while for low P (high W) it is 1.0620 +/- 0.0017. The weighted average of the two is 1.041 +/- 0.0013, so the systematics uncertainty is 4.1%.

Unlike the proton results on feb16, 2006, the errors for low P and high P are not close. ~~I feel I need to re-calculate the new PFs and do this study again.~~

overall deuteron DF systematics (updated from Sep.25 result)

[Update following the meeting on oct 30] Using the above systematic uncertainty of 4.1% due to A>2 nucleon model, the total deuteron DF systematic uncertainty is calculated. It is given by

delta_df = sqrt[(A*(delta_deuteron/deuteron))^2 + (B*(delta_nuclear/nuclear))^2 + (C*(delta_pf/pf))^2),
where A, B, and C are the scaling factors.

Deuteron model: Found that the relative DF systematic uncertainty due to deuteron model is 2.6% or less (Jul 03, 2007). A=1.0
Nuclear model: 4.0% change in the nuclear model (A>2) (=delta_nuclear/nuclear) yields 4.1% change in DF. B=1.025.
PF: Found that delta_pf/pf= ~8.2% (Sep25,2007). According to my Jul25,2005 report, 2.4% relative change in PF leads to 1.0% relative change in DF for deuteron target. Therefore, C is estimated to be C=1.0/2.4=0.417. The result is given below:

delta_df= sqrt[(2.6%)^2 + (4.1%)^2 + (0.417*8.2%)^2]= 5.94%

In addition, we can add other systematics due to run selection (0.5%, Jul25,2005) and PF extraction methods (0.4% Aug16,2005). The total DF systematics then becomes 5.97%.

Status and results (Sep. 25, 2007)

Study of deuteron DF Systematics uncertainties

Using the latest hbook files for PF results posted on Nov 01, 2006, the following table is generated for ND3-para-top configs. This corresponds to Table 1 of Oscar's PF/DF technote . note that Y = m pf* + b = m' pf*' + b', where m' and b' are scaled by carbon data/MC ratio, S, such that m'=S m and b'=S b.

A systematic uncertainty due to S is given by d(pf*')= -Y/m' dS/S (eq 14 of tech note). Assuming dS/S = 0.05 as for the proton systematics calculation (Feb09, 2006), d(pf*') can be determined.

Table 5: Integrated W yields for ND3-para-top (Scalein=1.0 )

S
(C.target
Data/MC)
Y
(Data)
Y_MC
(PF=50%)
Unscaled

Y_MC

(PF=60%)
Unscaled

m
(slope)
b
(intercept)
pf*
m'
(=S m)
b'
(=S b)
pf*'
d(pf*')

(due to S)
d(pf*')/pf*

(Rel.error)

High
pHMS
1.110
139.8
118.8
132.9
141.0
48.3
0.649
156.5
53.6
0.550
-0.0446
-8.11 %

Low
pHMS
1.075
269.8
239.7
268.1
284.0
97.7
0.606
305.3
105.0
0.540
-0.0441
-8.17 %

overall deuteron DF systematics (preliminary)

DF systematics can be calculated as

      delta_df = sqrt[(A*(delta_deuteron/deuteron))^2 + (B*(delta_nuclear/nuclear))^2 + (C*(delta_pf/pf))^2),

      where A, B, and C are the scaling factors.

Deuteron model: Found that the relative DF systematic uncertainty due to deuteron model is 2.6% or less (Jul 03, 2007). A=1.0
Nuclear model: 4% change in the nuclear model (A>2) yields ??? % change in DF. (in progress)
PF: Found that delta_pf/pf= ~8.2% (Sep25,2007). According to my Jul25,2005 report, 2.4% relative change in PF leads to 1.0% relative change in DF for deuteron target. Therefore, C is estimated to be C=1.0/2.4=0.417

(If we can assume deuteron DF systematics due to nuclear model is 3%, delta_df= sqrt[(2.6%)^2 + (3%)^2 + (0.417*8.2%)^2]= 5.2% (the same value as proton DF systematics)

In addition, we could also add other relative systematics uncertainties due to run selection (0.5%, Jul25,2005)and PF extraction methods (0.4% Aug16,2005). If we do so, the total DF systematics would increase by ~+0.1%.

Status and results (Jul. 03, 2007)

Study of DF Systematics uncertainty on deuteron model

Accroding to Peter (see his email on Jun07,2007), the deuteron uncertainty at Q2=1.3 for inelastic (Quasi-elastic) region is 3-4% (5%). To study the systematic effect on the deuteron cross section, the deuteron cross section is increased by 4% (inelastic) and 5%(quasi-elastic) and see how much DF changes. First, we obtained the PF for each target/momentum config. It became smaller by 0.6-1.0% because the cross section is increased. (Carbon rus are not affected by these changes so the Carbon Data/MC ratios remain the same as before.)

Table 1: ND3, TOP (modified Peter's model using F1F2IN06_rss.f and RSS ressf.f. QFS for A>2, scalein: 1.0)

Target(Run#)	pHMS (MeV/c)	Field	T/B	C(no He) Run#	Carbon Ratio (Data/MC)	PF(%)	W Range	Plots	AVG PF	PF increase
ND3 (43855)	4703 (HI)	Para	Top	43887	1.110+/-0.005	54.16+/-0.23	(1.2,1.5)	W ,Targ ,PF	53.6+/-0.15	-0.9%
ND3 (43950)	4078 (LO)	Para	Top	43743	1.075+/-0.004	53.18+/-0.20	(1.5,1.8)	W ,Targ ,PF	53.6+/-0.15	-0.9%
ND3 (43450)	4703 (HI)	Perp	Top	43400	---	not obtained	(1.2,1.5)	---	----	---
ND3 (43490)	4078 (LO)	Perp	Top	43547	---	not obtained	(1.5,1.8)	---	----	---

Table 2: ND3, Bot (modified Peter's model using F1F2IN06_rss.f and RSS ressf.f. QFS for A>2, scalein: 1.0)

Target(Run#)
pHMS
(MeV/c)
Field
T/B
C(no He)
Run#
Carbon Ratio
(Data/MC)
PF(%)

W Range
Plots
AVG PF
PF
increase

ND3 (43895)
4703 (HI)
Para
Bot
43887
1.110+/-0.005
57.59+/-0.26
(1.2,1.5) W ,Targ ,PF
55.2+/-0.16

-0.6%

ND3 (43939) 4078 (LO) Para Bot 43743 1.075+/-0.004 53.82+/-0.20 (1.5,1.8) W ,Targ ,PF

ND3 (43520)
4703 (HI)
Perp
Bot 43536
1.107+/-0.005 59.48+/-0.34 (1.2,1.5)
W ,Targ ,PF
60.0+/-0.23

-1.0%

ND3 (43550)
4078 (LO)
Perp
Bot 43547
1.063+/-0.004 60.48+/-0.31 (1.5,1.8)
W ,Targ ,PF

Using these PFs, new sets of DFs are obtained. Calculated the ratio of new DFs to the original DFs (dec11,2006) and take the average ratio for W>1100. The new PF became smaller by~1% but we increased the deuteron xsec by several percent. Therefore, the new DFs become larger by a few %. The ratios are 1.024+-0.001 (para-top), 1.028+-0.001 (para-bot),1.025+-0.001 (perp-bot). Taking the avg of the 'para' results, we have the ratios of 1.026(para) and 1.025(perp). That means DF uncertainty due to deuteron model is 2.6% for para and 2.5% for perp.

Status and results (Dec. 11, 2006)

Deuteron DFs using Peter's models

Three sets of deuteron models were tested recently (see Nov01, Nov13, Nov27 below) and they were compared to data. At the last meeting, we decided to use the Peter's deuteron models (Q.E. and inelastic) to get the DFs. QFS is still used for A>2. The christy806 routine is used to obtain R.

Results of deuteron DFs using Peter's models are given below. The AVG PFs obtained on Nov01 were used in the MC. The 1st and 2nd resonances are slightly clearer than before but the 3rd resonance is still not clear. Compared to the previous results(Mar02,'06) where the Hallc2h+yscaling were used for the deuteron, the DFs became smaller than the previous results even though the new PFs increased by 2-3%. I believe that's because Peter's models give smaller deuteron cross section but the decrease in the cross section is not fully canceled by the PF increase. The relative MAX difference between the new and previous DFs for hi-para is 21% at W=1100 MeV. Similarly, the relative difference at W=1235 is 9%.

DFs obtained from the indivisual HighP and LowP MC runs agree better than the previous (Mar02) results.

Table 1: ND3 Dilution Factors (Ver. Dec.11, 2006) -- Using Peter's models, scalein=1.0, AVG PFs

Target	Field	T/B	Avg PF(%)(Nov01 '06)	DF Results	Comments
ND3	Para	Top	54.5+/-0.2	Data, Plot,	Comparison of hi and lo DFs ,
ND3	Perp	Top	TBA	TBA
ND3	Para	Bot	55.8+/-0.2	Data, Plot
ND3	Perp	Bot	61.0+/-0.3	Data, Plot	Comparison of hi and lo DFs

Status and results (Nov. 27, 2006)

Comparison of data and MC (Peter's model with RSS ressf.f) (Follow up)

[The following text posted on Nov.13. Re-posted here for convenience] We want to check if the Peter's inelastic model(F1F2in06.f) with the ressf routine used in our RSS MC might work.The Christy806 routine called from the pind routine is replaced with the ressf_2.f so that we can see how the cross section depends on the choice of 'R'. Here is a plot of the deuteron cross section using this modified model. This plot shows the comparison of the fermi-smeared R from the christy806 and ressf.f routines.

The table below shows the PFs and model comparisons. Compared to the Mar02 results where our y-scaling and hallc2h.f routines are used, the AVG PFs increased by 2-3 %. If compared with the Nov01 results where peter's original models are used, the avg PFs become smaller by less than 1%.

This table also has the data-model comparison plots which can be compared with the Nov01 results where peter's original routines are used without modifications. Note that the differeces between those two results are due to the choice of R and avg PF values. We can say that the those two results are basically quite similar even though the R models are different.

Table 1: ND3, TOP (modified Peter's model using F1F2IN06_rss.f and RSS ressf.f. QFS for A>2, scalein: 1.0)

Target(Run#)	pHMS (MeV/c)	Field	T/B	C(no He) Run#	Carbon Ratio (Data/MC)	PF(%)	W Range	Plots	AVG PF	PF increase	Data-MC Comparison
ND3 (43855)	4703 (HI)	Para	Top	43887	1.110+/-0.005	54.44+/-0.23	(1.2,1.5)	W ,Targ ,PF	54.0+/-0.15	+2.3%	Data vs MC (using avg PF)
ND3 (43950)	4078 (LO)	Para	Top	43743	1.075+/-0.004	53.76+/-0.19	(1.5,1.8)	W ,Targ ,PF	54.0+/-0.15	+2.3%	Data vs MC (using avg PF)
ND3 (43450)	4703 (HI)	Perp	Top	43400	---	not obtained	(1.2,1.5)	---	----	---
ND3 (43490)	4078 (LO)	Perp	Top	43547	---	not obtained	(1.5,1.8)	---	----	---

Table 2: ND3, Bot (modified Peter's model using F1F2IN06_rss.f and RSS ressf.f. QFS for A>2, scalein: 1.0)

Target(Run#)
pHMS
(MeV/c)
Field
T/B
C(no He)
Run#
Carbon Ratio
(Data/MC)
PF(%)

W Range
Plots
AVG PF
PF
increase
Data-MC
Comparison

ND3 (43895)
4703 (HI)
Para
Bot
43887
1.110+/-0.005
57.89+/-0.27
(1.2,1.5) W ,Targ ,PF
55.6+/-0.16

+2.0%
Data vs MC
(using avg PF)

ND3 (43939) 4078 (LO) Para Bot 43743 1.075+/-0.004 54.42+/-0.19 (1.5,1.8) W ,Targ ,PF

ND3 (43520)
4703 (HI)
Perp
Bot 43536
1.107+/-0.005 59.79+/-0.36 (1.2,1.5)
W ,Targ ,PF
60.5+/-0.25

+2.6%
Data vs MC
(using avg PF)

ND3 (43550)
4078 (LO)
Perp
Bot 43547
1.063+/-0.004 61.17+/-0.34 (1.5,1.8)
W ,Targ ,PF

Status and results (Nov. 13, 2006)

Comparison of data and MC (Peter's model with RSS ressf.f)

We want to check if the Peter's inelastic model(F1F2in06.f) with the ressf routine used in our RSS MC might work.The Christy806 routine called from the pind routine is replaced with the ressf_2.f so that we can see how the cross section depends on the choice of 'R'. Here is a plot of the deuteron cross section using this modified model. This plot shows the comparison of the fermi-smeared R from the christy806 and ressf.f routines.

Comparison of data and MC (hallc2h.f with wpi=1.038)

Oscar said that the deuteron cross section using hallc2h.f with wpi=1.038 shows better agreement with the data than with wpi=0.982 that we've been using in the MC. I changed wpi to 1.038 and ran the MC to check. The y-scaling routine has not been changed. This plot shows the cross section using this modified model. The results of the data-model comparison for this model are given below. The 'PF increase' column shows how much the avg PF increased from the Mar02 results using wpi=0.982. The increase in the PF is about 0.5%. The results of the data-model comparison (the last column) are basically the same as the Oct09 results using wpi=0.982.

Table 1: ND3, TOP (using Hallc2h.f with Wpi=1.038. QFS for A>2, scalein: 1.0)

Target(Run#)	pHMS (MeV/c)	Field	T/B	C(no He) Run#	Carbon Ratio (Data/MC)	PF(%)	W Range	Plots	AVG PF	PF increase	Data-MC Comparison
ND3 (43855)	4703 (HI)	Para	Top	43887	1.110+/-0.005	52.7+/-0.24	(1.2,1.5)	W ,Targ ,PF	52.3+/-0.16	+0.6%	Data vs MC (using avg PF)
ND3 (43950)	4078 (LO)	Para	Top	43743	1.075+/-0.004	52.0+/-0.21	(1.5,1.8)	W ,Targ ,PF	52.3+/-0.16	+0.6%	Data vs MC (using avg PF)
ND3 (43450)	4703 (HI)	Perp	Top	43400	---	not obtained	(1.2,1.5)	---	----	---
ND3 (43490)	4078 (LO)	Perp	Top	43547	---	not obtained	(1.5,1.8)	---	----	---

Table 2: ND3, Bot (using Hallc2h.f with Wpi=1.038. QFS for A>2, scalein: 1.0)

Target(Run#)
pHMS
(MeV/c)
Field
T/B
C(no He)
Run#
Carbon Ratio
(Data/MC)
PF(%)

W Range
Plots
AVG PF
PF
increase
Data-MC
Comparison

ND3 (43895)
4703 (HI)
Para
Bot
43887
1.110+/-0.005
55.9+/-0.22
(1.2,1.5) W ,Targ ,PF
54.1+/-0.15

+0.5%
Data vs MC
(using avg PF)

ND3 (43939) 4078 (LO) Para Bot 43743 1.075+/-0.004 52.7+/-0.20 (1.5,1.8) W ,Targ ,PF

ND3 (43520)
4703 (HI)
Perp
Bot 43536
1.107+/-0.005 57.7+/-0.27 (1.2,1.5)
W ,Targ ,PF
58.5+/-0.19

+0.6%
Data vs MC
(using avg PF)

ND3 (43550)
4078 (LO)
Perp
Bot 43547
1.063+/-0.004 59.3+/-0.27 (1.5,1.8)
W ,Targ ,PF

Status and results (Nov. 01, 2006)

Comparison of deuteron data and MC using Peter's models

Thanks to Peter, we now have his deuteron QE and inelastic routines. The plot of deuteron cross sections at thetae=13.15 deg(fixed) shows that the peter's models are basically below our current models(Y-scaling + Hallc2h routines). [Note: Peter's routines say that the outputs F1 and F2 are per NUCLEUS values, NOT per nucleon.] I ran the MC with his routines to see if they are better than what we have been using. First, we obtained the new PFs, and then reran the MC with the new PFs to make a comparison with the data. The results are given below.

Table 1: ND3, TOP (Peter's QE+inelastic models. QFS for A>2, scalein: 1.0)

Target(Run#)	pHMS (MeV/c)	Field	T/B	C(no He) Run#	Carbon Ratio (Data/MC)	PF(%)	W Range	Plots	AVG PF	PF increase	Data-MC Comparison
ND3 (43855)	4703 (HI)	Para	Top	43887	1.110+/-0.005	55.0+/-0.23	(1.2,1.5)	W ,Targ ,PF	54.5+/-0.2	+2.8%	Data vs MC (using avg PF)
ND3 (43950)	4078 (LO)	Para	Top	43743	1.075+/-0.004	54.0+/-0.19	(1.5,1.8)	W ,Targ ,PF	54.5+/-0.2	+2.8%	Data vs MC (using avg PF)
ND3 (43450)	4703 (HI)	Perp	Top	43400	---	not obtained	(1.2,1.5)	---	----	---
ND3 (43490)	4078 (LO)	Perp	Top	43547	---	not obtained	(1.5,1.8)	---	----	---

Table 2: ND3, Bot (Peter's QE+inelastic models. QFS for A>2, scalein: 1.0)

Target(Run#)
pHMS
(MeV/c)
Field
T/B
C(no He)
Run#
Carbon Ratio
(Data/MC)
PF(%)

W Range
Plots
AVG PF
PF
increase
Data-MC
Comparison

ND3 (43895)
4703 (HI)
Para
Bot
43887
1.110+/-0.005
58.5+/-0.29
(1.2,1.5) W ,Targ ,PF
55.8+/-0.2

+2.2%
Data vs MC
(using avg PF)

ND3 (43939) 4078 (LO) Para Bot 43743 1.075+/-0.004 54.6+/-0.19 (1.5,1.8) W ,Targ ,PF

ND3 (43520)
4703 (HI)
Perp
Bot 43536
1.107+/-0.005 60.4+/-0.39 (1.2,1.5)
W ,Targ ,PF
61.0+/-0.3

+3.1%
Data vs MC
(using avg PF)

ND3 (43550)
4078 (LO)
Perp
Bot 43547
1.063+/-0.004 61.4+/-0.35 (1.5,1.8)
W ,Targ ,PF

Note that I still use QFS for A>2 because the agreement with the data is good. So, the carbon ratios as well as the carbon 'W' and 'target' plots in the above tables are the same as those on Mar02, 2006. (In other words, only the RED numbers are the new results.) The AVG PFs increased by 2-3% compared to the Mar02 results where our current models were used. That was because the peter's models are lower than our current models as mentioned above.

The data-MC compasison plots in the last column can be compared with those deuteron plots posted on Oct 09, 2006 below. For para, the Peter's models are better than our current models especially for W<1.2GeV. For W>1.2GeV, both results look similar by eye. For perp, our current models look silightly better than the Peter's models.

Status and results (Oct. 09, 2006)

Comparison of data and MC (Proton, Deuteron)

Here are the updated plots of yields showing the comparison between the proton from MC vs "data-MC(no proton)", and similarly for the deuteron. The avg of the PFs from the low and high P runs was used in each case. In the overlap region of W (W~1.5 GeV), MC yield is larger than the data which cause a dip around that W region in the ratio plot. If we look at an individual high P (low P) data with the MC, we found that the MC yield is larger than the data for W>1.5 (W<1.5). Therefore, the disagreement at W~1.5 is enhanced when high and low P runs are combined.

NOTE: The previous study was posted on Dec.15, 2005.

Table 1: Comparison of data and MC:

	Field	T/B	AVG of Lo-P & Hi-P PFs	Comparison of data and MC	Models used
Proton	para	top	53.2% (Feb 02, 2006)	MC(proton) vs Data-MC(no P)	Proton: Eric's (7/22/2005) inelastic models
Proton	perp	top	57.2% (Feb 02, 2006)	MC(proton) vs Data-MC(no P)	Proton: Eric's (7/22/2005) inelastic models
Deuteron	para	top	51.7% (Mar 02, 2006)	MC(deuteron) vs Data-MC(no D)	Deuteron: Y-scaling (QE) and Hallc (inelastic) models
Deuteron	perp	bot	57.9% (Mar 02, 2006)	MC(deuteron) vs Data-MC(no D)	Deuteron: Y-scaling (QE) and Hallc (inelastic) models

Note: Due to the changes made by the Computer center this summer, I had to change the batch script for submitting jobs slightly. The following changes were made to the submit_replay script I have. Add 'TRACK: analysis' and 'PROJECT: e01006'. Comment out or remove the 'QUEUE' line. Below are the lines from the updated script.

# echo 'QUEUE: production'   >> bat_files/jsub_file_$nrun
   echo 'TRACK: ANALYSIS'     >> bat_files/jsub_file_$nrun
   echo 'PROJECT: e01006'     >> bat_files/jsub_file_$nrun

Status and results (Mar. 02, 2006)

Deuteron PFs and Dilution factors

Because QFS was modified last Dec, the deuteron PFs and DFs are updated. Compared to the previous sets of ND3 PFs (Jul08), the PFs became smaller by about 1.5%. I also tried calculating PFs for perp-top without any cuts on target raster positions, and the PFs became smaller by ~2%. I will apply cuts and determine the PFs for these cases.

Table 1: ND3, TOP (QFS for A>2, scalein: 1.0)

Target(Run#)	pHMS (MeV/c)	Field	T/B	C(no He) Run#	C. Ratio (Data/MC)	PF(%)	W Range	Plots	AVG PF	PF difference (Hi P- LowP)
ND3 (43855)	4703 (HI)	Para	Top	43887	1.110+/-0.005	51.9+/-0.25	(1.2,1.5)	W ,Targ ,PF	51.7+/-0.2	0.3%
ND3 (43950)	4078 (LO)	Para	Top	43743	1.075+/-0.004	51.6+/-0.21	(1.5,1.8)	W ,Targ ,PF	51.7+/-0.2	0.3%
ND3 (43450)	4703 (HI)	Perp	Top	43400	1.094+/-0.005	(60.5+/-0.42)TBA	(1.2,1.5)	W ,Targ ,PF	(62.2+/-0.3) TBA
ND3 (43490)	4078 (LO)	Perp	Top	43547	1.063+/-0.004	(64.2+/-0.46)TBA	(1.5,1.8)	W ,Targ ,PF	(62.2+/-0.3) TBA

Table 2: ND3, Bot (QFS for A>2, scalein: 1.0)

Target(Run#)
pHMS
(MeV/c)
Field
T/B
C(no He)
Run#
C. Ratio
(Data/MC)
PF(%)

W Range
Plots
AVG PF
PF difference
(Hi P - LowP)

ND3 (43895)
4703 (HI)
Para
Bot
43887
1.110+/-0.005
55.1+/-0.22
(1.2,1.5) W ,Targ ,PF 53.6+/-0.2 2.8%

ND3 (43939) 4078 (LO) Para Bot 43743 1.075+/-0.004 52.3+/-0.21 (1.5,1.8) W ,Targ ,PF

ND3 (43520)
4703 (HI)
Perp
Bot 43536
1.107+/-0.005 56.9+/-0.25 (1.2,1.5)
W ,Targ ,PF 57.9+/-0.2 -2.0%

ND3 (43550)
4078 (LO)
Perp
Bot 43547
1.063+/-0.004 58.9+/-0.25 (1.5,1.8)
W ,Targ ,PF

Like the NH3 DF calculation, the AVG of the PFs from low-P and high-P runs is used in the DF calculation. Good agreement for lower W compared to the previous DF data, but up to 7% change at higher W.

Table 3: ND3 Dilution Factors (Ver. Mar02) -- Using QFS(A>2), scalein=1.0, AVG PFs

Target	Field	T/B	AVG PF(%)	Results	Comments
ND3	Para	Top	51.7+/-0.2	Data, Plot,	Comparison of hi and lo DFs ,
ND3	Perp	Top	TBA	TBA
ND3	Para	Bot	53.6+/-0.2	Data, Plot
ND3	Perp	Bot	57.9+/-0.3	Data, Plot	Comparison of hi and lo DFs

Status and results (Feb. 16, 2006)

Updated proton DF systematics

Some of the systematic errors in DF are updated. The updated nuclear model uncertainty by Oscar is 4%, and the PF uncertainty is 1.77*5% (Feb 15). Eric confirmed (Feb15) that the proton model systematic from the E94-110 data set is 3%. Therefore, the delta_df in eq.[2] of my Feb09 report becomes

delta_df = sqrt[(0.64*3%)^2 + (0.73*4%)^2 + (0.37*1.77*5%)^2 = 4.8%

Relative systematics uncertainty due to run selection is 0.8%(unchanged) (jul25). Relative systematics due to PF extraction is 0.5% (average of para and perp results)(aug16). The total systematics including these is delta_df = 4.9%.

Status and results (Feb. 09, 2006)

Update on the DF systematics from the nuclear model (Follow up on the Jan26 results)

I recalculated the DF systematics by comparing the DFs with scalein=1.0 and with scalein=1.04,0.96. But this time, I compared the high-p runs and low-p runs saparately, and made a weighted-average of the two. The systematics errors for W>1100 are 2.4+-0.3% for high-p runs, and 3.3+-0.3% for low-p runs. The average of the two is 2.9+-0.2%. In summary, the 4% change in nuclear model would yield 2.9% change in DF.

Summary of the proton DF systematics

DF systematics can be calculated as

      delta_df = sqrt[(A*(delta_proton/proton))^2 + (B*(delta_nuclear/nuclear))^2 + (C*(delta_pf/pf))^2),

      where A, B, and C are the ratios of the changes in DF due to proton model, nuclear model, and PF:

A: 10% change in the proton model yields 6.4% change in DF. A=6.4/10 = 0.64. (Dec 01)
B: 4% change in the nuclear model yields 2.9% change in DF. B=2.9/ 4 = 0.73. (Feb 09)
C: On Jul 25, I reported that the "2.5% change in PF leads to 1.7% change in DF". But the 2.5% change was just the difference between two PFs. Therefore, my statement means "2.5% ABSOLUTE change in PF (or 4.5% RELATIVE change in PF) leads to 1.7% RELATIVE change in DF". Therefore, the factor C=1.7%/4.5% = 0.37. delta_pf/pf can be calculated from eq. (14) of Oscar's PF tech note. Using the values for scalein=1.0 from Table 1 of the tech note and also assuming dS/S=5%, delta_pf/pf = -8.5%.

Assuming proton model and nuclear model have uncertainties 3% and 5% respectively,

delta_df = sqrt[(0.64*3%)^2 + (0.73*5%)^2 + (0.37*8.5%)^2 = 5.2%

In addition, we could also add other systematics (~1%) due to run selection and PF extraction methods as summarized in table 1 of my Dec 1 report. If we do so, the total systematics is 5.3%.

Plan to write a more 'formal' report summarizing the total DF systematics.

Status and results (Feb. 02, 2006)

New proton PFs & DFs

QFS was updated by Oscar and Mark this week. (sig0 in qfs routine 'sigx' gets multiplied by 0.92 : sig0=100.d-4*.92 )

Almost no change in PFs for hi p runs, ~0.4% change for low p runs. The C ratio (=Data/MC) for low p run became larger by about 2.5% because the DIS component of QFS became smaller.

The AVG PFs became smaller by ~0.2% than the previous PFs (12/22).

Table 1: NH3, TOP (QFS for A>2, scalein: 1.0)

Target(Run#)	pHMS (MeV/c)	Field	T/B	C(no He) Run#	C. Ratio (Data/MC)	PF(%)	W Range	Plots	AVG PF	PF difference (Hi P- LowP)
NH3 (43724)	4703 (HI)	Para	Top	43774	1.126+/-0.005	55.0+/-0.2	(1.2,1.5)	W ,Target ,PF	53.2+/-0.2	3.9%
NH3 (43740)	4078 (LO)	Para	Top	43743	1.075+/-0.003	51.1+/-0.3	(1.5,1.8)	W ,Target ,PF	53.2+/-0.2	3.9%
NH3 (43261)	4703 (HI)	Perp	Top	43284	1.101+/-0.006	57.0+/-0.3	(1.2,1.5)	W ,Target ,PF	57.2+/-0.2	-0.4%
NH3 (43369)	4078 (LO)	Perp	Top	43361	1.078+/-0.004	57.4+/-0.3	(1.5,1.8)	W ,Target ,PF	57.2+/-0.2	-0.4%

Table 2: NH3, Bot (QFS for A>2, scalein: 1.0)

Target(Run#)
pHMS
(MeV/c)
Field
T/B
C(no He)
Run#
C. Ratio
(Data/MC)
PF(%)

W Range
Plots
AVG PF
PF difference
(Hi P - LowP)

NH3 (43801)
4703 (HI)
Para
Bot
43774
1.126+/-0.005
57.1+/-0.3
(1.2,1.5) W ,Target ,PF 54.2+/-0.2 5.2%

NH3 (43737) 4078 (LO) Para Bot 43743 1.075+/-0.003 51.9+/-0.2 (1.5,1.8) W ,Target ,PF

NH3 (43286)
4703 (HI)
Perp
Bot 43284
1.101+/-0.006 60.4+/-0.4 (1.2,1.5)
W ,Target ,PF 60.0+/-0.3 0.8%

NH3 (43364)
4078 (LO)
Perp
Bot 43361
1.078+/-0.004 59.6+/-0.3 (1.5,1.8)
W ,Target ,PF

Table 3: NH3 Dilution Factors (Ver. Feb02) -- Using Eric's model(7/22), QFS(A>2), scalein=1.0, AVG PFs(02/02)

Target	Field	T/B	AVG PF(%)	Results	Comments
NH3	Para	Top	53.2+/-0.2	Data, Plot,	Comparison of hi and lo DFs ,
NH3	Perp	Top	57.2+/-0.2	Data, Plot
NH3	Para	Bot	54.2+/-0.2	Data, Plot	Comparison of hi and lo DFs ,
NH3	Perp	Bot	60.0+/-0.3	Data, Plot

The change in DF compared to the previous (12/22) version is quite small (<1%) for W<1700, and about 3% for high W (w>1800). As usual, DFs for W<1100 have been replaced with those obtained from elastic data.

Status and results (Jan. 26, 2006)

Systematics uncertainty in Dilution Factors due to Scalein values

Proton DFs were calculated using the MC with scalein=1.04(high P) and 0.96(low P). As we found out on Dec20, the average PFs for this case were almost identical to those with scalein=1.0 (see Tables on the Dec20 report below). The ratio of DFs were obtained and the difference from 1.0 gives the estimate of the systematic uncertainty. The ratio plots for Top-para , Top-perp show that the avg difference for w>1100 is 2.0%. The absolute values of the ratio were used to calculate the average deviation which gives the estimate of the systematic error. For high P (low W), the DFs calculated with scalein=1.04 become smaller because the A>2 cross section was increased. That results in the ratio value smaller than 1.0. Similarly for low P (high W), the DF becomes larger because of smaller A>2 cross section due to scalein=0.96, and the ratio becomes larger than 1.0. The systematic uncertainty in DFs due to the A>2 cross section (QFS) is estimated to be 1.0% for both para and perp.

Status and results (Dec. 22, 2005)

NH3 Dilution Factors obtained using the latest MC

Using the AVG PFs given in Tables 1 and 2 from the Dec20 report, new NH3 DFs were calculated. As before, the DFs for W<1100 MeV in the data files have been replaced with those from the elastic data. We still see good agreement at W=1100 MeV where the two DF sets meet (red and black points in the plots).

Table 1: NH3 Dilution Factors (Ver. Dec22) -- Using Eric's model(7/22), QFS(A>2), scalein=1.0, AVG PFs(12/20)

Target	Field	T/B	AVG PF(%)	Results	Comments
NH3	Para	Top	53.4+/-0.2	Data, Plot,
NH3	Perp	Top	57.5+/-0.2	Data, Plot
NH3	Para	Bot	54.3+/-0.2	Data, Plot
NH3	Perp	Bot	60.2+/-0.3	Data, Plot

Status and results (Dec. 20, 2005)

NH3 Packing Fractions obtained using the latest MC

Mark found and fixed a bug in mc_hms_single.f on Dec16. We ran the updated MC using scalein=1.0 like we did last week (Dec09). The PFs with QFS for A>2 are given in Tables 1 and 2. The PFs using Peter's model for A>2 were also obtained but not shown.

Table 1: NH3, TOP (QFS for A>2, scalein: 1.0)

Target(Run#)
pHMS
(MeV/c)
Field
T/B
C(no He)
Run#
C. Ratio
(Data/MC) PF(%)
W Range
Plots
AVG PF
PF difference
(Hi P- LowP)

NH3 (43724)
4703 (HI)
Para
Top
43774
1.119+/-0.005 55.1+/-0.2 (1.2,1.5) W ,Target ,PF 53.4+/-0.2
3.6%

NH3 (43740) 4078 (LO) Para Top 43743 1.049+/-0.003
51.5+/-0.3 (1.5,1.8) W ,Target ,PF

NH3 (43261)
4703 (HI)
Perp
Top
43284
1.094+/-0.006
57.1+/-0.3 (1.2,1.5) W ,Target ,PF 57.5+/-0.2
-0.7%

NH3 (43369)
4078 (LO)
Perp
Top
43361
1.051+/-0.004
57.8+/-0.3 (1.5,1.8)
W ,Target ,PF

Table 2: NH3, Bot (QFS for A>2, scalein: 1.0)

	S (C.target Data/MC)	Y (Data)	Y_MC (PF=50%) Unscaled	Y_MC (PF=60%) Unscaled	m (slope)	b (intercept)	pf*	m' (=S m)	b' (=S b)	pf*'	d(pf*') (due to S)	d(pf')/pf (Rel.error)
High pHMS	1.110	139.8	118.8	132.9	141.0	48.3	0.649	156.5	53.6	0.550	-0.0446	-8.11 %
Low pHMS	1.075	269.8	239.7	268.1	284.0	97.7	0.606	305.3	105.0	0.540	-0.0441	-8.17 %